Sensitivity analysis of echo state networks for forecasting pseudo-periodic time series

This paper presents an analysis of the impact of the parameters of an Echo State Network (ESN) on its performance. In particular, we are interested on the parameter behaviour when the model is used for forecasting pseudo-periodic time series. According previous literature, the spectral radius of the hidden-hidden weight matrix of the ESN is a relevant parameter on the model performance. It impacts in the memory capacity and in the accuracy the model. Small values of the spectral radius are recommended for modelling time-series that require short fading memory. On the other hand, a matrix with spectral radius close to the unity is recommended for processing long memory time series. In this article, we figure out that the periodicity of the data is also an important factor to consider in the design of the ESN. Our results show that the better forecasting (according to two metrics of performance) occurs when the hidden-hidden weight matrix has spectral value equal to 0.5. For our analysis we use a public synthetic dataset that has a high periodicity.